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Signal Theory, 6 credits
Signalteori, 6 hp
TSDT14
Main field of study
Electrical EngineeringCourse level
Second cycleCourse type
Programme courseExaminer
Mikael OlofssonDirector of studies or equivalent
Klas NordbergEducation components
Preliminary scheduled hours: 54 hRecommended self-study hours: 106 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Electrical EngineeringCourse level
Second cycleAdvancement level
A1XCourse offered for
- Biomedical Engineering, Master's Programme
- Communication Systems, Master's Programme
- Computer Science and Engineering, M Sc in Engineering
- Industrial Engineering and Management - International, M Sc in Engineering
- Electronics Design Engineering, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Information Technology, M Sc in Engineering
- Biomedical Engineering, M Sc in Engineering
- Computer Science and Software Engineering, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
From Calculus: Derivatives and integrals.From Probability theory: Most, but with focus on binary distributions, rectangular distributions and Gaussian distributions.
From Signals and systems: Fourier transforms, LTI systems, convolution, amplitude modulation, sampling and pulse amplitude modulation. (all of it deterministic)
Intended learning outcomes
After passing the course, the student should
- be able to clearly define central concepts regarding stochastic processes, using own words.
- be able to reliably perform standard calculations regarding stochastic processes, e.g. LTI filtering (both time continuous and time discrete), sampling and pulse amplitude modulation, but also certain momentary non-linearities that are common in telecommunication.
- with some reliability be able to solve problems that demand integration of knowledge from different parts of the course, i.e. analysis of LTI-filtering, modulation, sampling and non-linear filtering of stochastic processes, both one-dimensional and multi-dimensional.
- be able to account for the connection between different concepts in the course in a structured way using adequate terminology.
- be able to estimate the auto correlation function and power spectral density of a stochastic process based on a realization of the process. Also, clearly and logically account for those estimations and conclusions that can be drawn from them.
Course content
- Time continuous and time discrete stochastic processes: Probability distribution, probability density, expectation, ensemble expectation, auto correlation function, power spectral density, cross correlation function, cross spectral density, stationarity, ergodicity. Especially Gaussian processes and white processes. Multidimensional processes.
- LTI filtering of stochastic processes: Relations between statistical properties of the input process and the output process. Especially matched filters and white Gaussian noise as input.
- Amplitude and angle modulation of stochastic processes: Relations between statistical properties of the input process and the output process. Especially Gaussian processes as input. Noise analysis of those modulation forms, primarily with white Gaussian noise as disturbance.
- Non-linear momentary systems: Quantization and monomial non-linearities. Relations between statistical properties of the input process and the output process. Especially Gaussian processes as input. Properties of quantization noise.
- Transformation between time continuous and time discrete stochastic processes: Sampling and pulse amplitude modulation, the sampling theorem, reconstruction and reconstruction error.
- Case study: Reconstruction in CD players.
- Estimation of expectations, auto correlation function and power spectral density.
Teaching and working methods
Teaching is given in the form of lectures, tutorial and laborations
Examination
| LAB1 | Laboratory Work | 2 credits | U, G |
| TEN1 | Written Examination | 4 credits | U, 3, 4, 5 |
At the exam, there will be an introductory task that examines the learning outcomes "be able to clearly define..." and " be able to reliably perform standard calculations...". This task has to be solved correctly, in order to pass the exam. The rest of the exam examines the learning outcome " with some reliability be able to solve problems...". The grade on the exam, and also on the course as a whole is based on this part.
The laborations are performed in small groups and is examined based on a report. This examines the last two learning outcomes, " be able to account for..." and " be able to estimate...".
The laborations are performed in small groups and is examined based on a report. This examines the last two learning outcomes, " be able to account for..." and " be able to estimate...".
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Digital Communication Continuation Course, Radio communication, Data compression, Image and audio coding, Communication systems CDIO.
Department
Institutionen för systemteknikDirector of Studies or equivalent
Klas NordbergExaminer
Mikael OlofssonCourse website and other links
http://www.commsys.isy.liu.se/en/student/kurser/TSDT14Education components
Preliminary scheduled hours: 54 hRecommended self-study hours: 106 h
Course literature
Additional literature
Books
- Mikael Olofsson, (2011) Signal Theory
ISBN: 978-91-44-07353-8
Studentlitteratur - Mikael Olofsson, (2011) Tables and Formulas for Signal Theory
ISBN: 978-91-44-07328-6
Studentlitteratur
Compendia
Additional problems and Lab Memo will be distributed during the course.
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| LAB1 | Laboratory Work | 2 credits | U, G |
| TEN1 | Written Examination | 4 credits | U, 3, 4, 5 |
At the exam, there will be an introductory task that examines the learning outcomes "be able to clearly define..." and " be able to reliably perform standard calculations...". This task has to be solved correctly, in order to pass the exam. The rest of the exam examines the learning outcome " with some reliability be able to solve problems...". The grade on the exam, and also on the course as a whole is based on this part.
The laborations are performed in small groups and is examined based on a report. This examines the last two learning outcomes, " be able to account for..." and " be able to estimate...".
The laborations are performed in small groups and is examined based on a report. This examines the last two learning outcomes, " be able to account for..." and " be able to estimate...".
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Books
Mikael Olofsson, (2011) Signal Theory
ISBN: 978-91-44-07353-8
Studentlitteratur
Mikael Olofsson, (2011) Tables and Formulas for Signal Theory
ISBN: 978-91-44-07328-6
Studentlitteratur
Compendia
Additional problems and Lab Memo will be distributed during the course.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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LAB1
TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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X
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LAB1
TEN1
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||
| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
|
X
|
|
LAB1
TEN1
|
||
| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
X
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X
|
LAB1
TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
|
X
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LAB1
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
|
X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
|
X
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X
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LAB1
TEN1
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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LAB1
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| 3.2 Communications |
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X
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LAB1
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| 3.3 Communication in foreign languages |
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X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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